The heat transfer and flow attributes of a cylindrical microchannel heat sink (CMCHS) operated with a hybrid nanofluid containing the graphene nanoplatelets and platinum particles are numerically investigated. The CMCHS is modeled with three different numbers of fins, and the problem is solved for four concentrations and four Reynolds numbers. The effect of these variables on the thermal and frictional parameters—such as the convective heat transfer coefficient, pressure loss, friction coefficient, thermal resistance, and maximum temperature—is evaluated. The heat transfer coefficient increases by raising the Reynolds number, concentration, and fin number. Thereby, with an increase in fin number from 25 to 36 at Reynolds number of 300 and concentration of 0.1%, the convective heat transfer coefficient is enhanced by 134%. The maximum performance evaluation criterion (PEC) is obtained as 1.98 at concentration of 0.1%, Reynolds number of 600, and number of fins of 36. The thermal resistance decreases by increasing each of the parameters of fin number, Reynolds number, and concentration. Based on the obtained data, a predictor model for the output parameters (i.e., heat transfer coefficient, thermal resistance, and pumping power) is derived by a neural network. Then, the optimization is performed using a genetic algorithm combined with decision-making technique considering different designer’s viewpoints to achieve the highest convective heat transfer coefficient and the lowest pumping power and thermal resistance.

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